Feedback control circuit for magnetic suspension and propulsion system

ABSTRACT

A linear motor uses the same magnetic flux for suspension and propulsion of a high speed tracked vehicle and operates below a support rail without physical contact therewith. Displacement and inertial sensors carried by the vehicle sense the length of the motor-to-rail gap and any acceleration of the vehicle causing changes in the gap. A non-linear feedback circuit responds to the sensor signals and controls the voltage applied to the phased windings of the motor to maintain the selected gap. The feedback circuit provides uniform stability and dynamic response over a wide range of gap, maintains the selected gap substantially constant notwithstanding track irregularities and variations in vehicle loading, and gradually corrects for unevenness. The inertial sensor is made to be sensitive to vertical acceleration of the vehicle and insensitive to irregularities of the rail thereby assuring a &#39;&#39;&#39;&#39;smooth&#39;&#39;&#39;&#39; or &#39;&#39;&#39;&#39;easy&#39;&#39;&#39;&#39; ride notwithstanding irregularities of the rail. The frequency of the applied voltage is varied upwards from zero to adjust the linear speed of the motor, and the voltage is increased with the frequency to compensate for the increase in inductive reactance of the windings. A wide dynamic range of motor control voltage is provided to cover the propulsion range from standstill to high speed without requiring a wide dynamic range in the feedback control elements.

United States Patent 1191 Ross 45] June 5, 1973 Primary Examiner.1. D.Miller Assistant Examiner-H. Huberfeld AttorneyGeorge E. Pearson [75]Inventor: James A. Ross, La .lolla, Calif. [57] ABSTRACT [73] Assignee:Rohr Industries Inc., Chula Vista, A linear motor uses the same magneticflux for Calif. suspension and propulsion of a high speed trackedvehicle and operates below a support rail without [22] 1972 physicalcontact therewith. Displacement and inertial [2]] App]. No.: 219,713sensors carried by the vehicle sense the length of the motor-to-rail gapand any acceleration of the vehicle Related U-s. Application Datacausing changes in the gap 1 continuatiomin-pal't 0f 1311041, April 16,A non-linear feedback circuit responds to the sensor 971, Pu 3,638,093signals and controls the voltage applied to the phased windings of themotor to maintain the selected gap. 1 318/537, The feedback circuitprovides uniform stability and 318/687 dynamic response over a widerange of gap, maintains [51] Int. Cl. .L ..I-I02k 41/02 the ele ted gasubstantially constant notwithstand- [5 Field of Search ing trackirregularities and variations in vehicle load- /8 ing, and graduallycorrects for unevenness.

91,93,148 R, 148 LM,l48 MS The inertial sensor is made to be sensmve tovert1cal [56] References Cited acceleration of the vehicle and 1nsens1t1ve to irr gular1t1es of the rail thereby assuring a smooth or UNITEDSTATES PATENTS easy ride notwithstanding irregularities of the rail.

3,102,217 8/1963 Bullen ..3l8/676X The frequency of the pp voltage isvaried "P- 3,660,745 5 1972 Bertrand ..3l8/676 wards r zero t adjust thelinear s eed of the mo- 3 125 964 3/1964 Silverman "104/148 MS x tor,and the voltage is increased with e frequency to 3:158:765 11/1964"318/135 x compensate for the increase in inductive reactance of3,407,749 10/1968 Frig ..31s/135 x the wmdmgs- 3,549,966 12/1970 Wilson..3l8/l35 A wide d f ynamlc range 0 motor control voltage 1s pro-3,611,944 10 1971 Reder ..104/l48 LM x vided to cover the propulsionrange from standstill to FOREIGN PATENTS OR APPLICATIONS high speedwithout requiring a wide dynamic range in the feedback control elements.1,035,764 7/1966 Great Britain ..l04/148 LM 1,537,842 7/1967 France 37Claims, 13 Drawing Figures 643,316 4/1937 Germany 1 1 104/148 MS 707,0326/1941 Germany ..104/148 MS SA 1 SA 2 1 1 VEHICLE S 1 F F 2 2 .iiiji i ki i l .1. b 211 I I l i 1 i \Rl L I R A i i l 1 I 1 F 2 h 1 1 M T M 1 10 0 2 01 02 PAIENIEDIIIII 5|975 3.736.880

SHEET 20F 8 COMPENSATING -4v SQUARE RooT R T ACCELE OME ER NETWORKcIRcuIT l f22 23 POSITION COMPENSATING TRANSDUCER NETWORK MULTIPLIER X(D.C. PATH) g95 96 AMPLIFIER PERFECT DIFFERENTIATOR rA.c. PATH) VEHICLE{RAIL 2 I 1. CONTROLABLE I f POWER 1 MOTOR SUPPLY PowER PAIENTEDJUH 5I975 SHEET 8 BF 8 w GI NI uZm3GwmE FEEDBACK CONTROL CIRCUIT FOR MAGNETICSUSPENSION AND PROPULSION SYSTEM CROSS-REFERENCE TO RELATED APPLICATIONSThis application is a continuation-in-part of the U.S. Pat. applicationof James A. Ross for Magnetic Suspension and Propulsion System, Ser. No.131,041,

filed Apr. 16, 1971, now U.S. Pat. No. 3,638,093, hereinafter sometimesreferred to as the parent application.

BACKGROUND OF THE INVENTION Heretofore others have suggested linearmotors utilizing the same magnetic flux for suspension and propulsion oftracked vehicles. United States Pat. No. 782,312 (1905) to Alfred Zehdenand French Pat. No. 1,537,842 (1968) to Jeumont-SchneiderElectromechanical Construction Company, for example, teach combinedpropulsion and suspension of a linear induction motor by magneticattraction of the motor upwardly toward its support rail which alsoserves as the reaction rail. Zehden discloses triphase windings, and theFrench patent teaches changes in power frequency to effect changes inpropulsion speed. The French patent further teaches the use of gapsensing operative in an electronic feedback circuit for maintainingsuspension of the motor below its support rail at a controlled air gaptherebetween, thereby to avoid physical contact with the rail both atstandstill and during propulsion along the rail. Zehden employs a railengaging wheel support and does not disclose a feedback control circuit.

German Pat. Nos. 643,316 (1937), 44,302 (1938), and 707,032 (1941) toHermann Kemper disclose the suspension of tracked vehicles by use ofelectromagnets disposed below a support rail and magnetically attractedthereto while maintaining a controlled air gap therebetween, thusavoiding physical contact of the electromagnets with the rail.

The 1941 Kemper patent and the French patent disclose similararrangements utilizing magnetic attraction for guidance and switching ofthe magnetically suspended vehicle.

The 1937 Kemper patent suggests that the electromagnets used forsuspension can be configured for polyphase operation for propulsion ofthe vehicle along the track, operating for this purpose in the manner ofpolyphase induction motors. Recent developments of German industry inthe transportation field, however, while apparently following theteachings of Kemper with respect to achieving magnetic suspension, tendto follow Kempers suggested alternative propulsion arrangement of usingseparate electromagnets operative with their own reaction rail in aconventional polyphased linear induction motor mode.

The suspension arrangement of the 1938 Kemper patent (Addition to the1937 patent), in common with the teaching of the 1937 patent, sensesmotor position with respect to the rail (gap), but further senses rateof change of that position (motor velocity), and change in motor energystate (motor suspension current) to provide a motor control voltagewhich is operative over a wide range of gap X (twice normal gap a). Themotor voltage may be d.c. or ac. and is characterized as being positiveor negative over-voltages for achieving arbitrarily high acceleration ofthe energy level contained in the motor windings.

The 1938 Kemper patent is concerned with providing feedback forpreventing oscillations of the suspended vehicle caused by the kineticenergy acquired by the vehicle in response to a correction of positionand, further, in preventing high acceleration of change of motor energylevel from causing further changes in energy level when the correctlevel is reached. The position feedback voltage e, produces a directingmagnetic force to return the suspended vehicle to the correct locationrelative to the rails, and the damping or velocity feedback voltage eassures that the correcting movement can be made to a more or lessdamped oscillation. A report feedback potential e, is made to beproportional to the motor current and, in turn, provides a measure ofthe momentary energy state of the motor magnet. The sum of the positionfeedback voltage e and the damping voltage e constitutes a commandvoltage e, which starts the energy addition or reduction when a changein gap is sensed. The report potential e, opposes the command potentiale to prevent further changes in the energy state as soon as the correctlevel is reached.

The feedback provided by the Kemper Addition Patent is made to produce asmooth ride of the suspended vehicle by designing a pull force curve(curve 111 of FIG. 4) wherein position feedback voltage e is caused tofall off for increasing gap distance, the directional pull force beingsufficient, however, to return the vehicle to the correct location butbeing limited to a desirable maximum value which results in limiting thetracking of the vehicle in relation to the rail track when movingrapidly. Additional absorption of rail nonuniformities is achieved byavoiding excessive suppression of the electrical inertia characteristicsof the feedback regulator circuits, the smooth ride resulting becausethe feedback is not required to force distance corrections fordeviations which exist only in short sections of the rail track wherebythe vehicle is caused to follow only the average from a number ofdifferent regulation impulses.

Automotive News for October 1970 describes an active spring-hydraulicsuspension system for an air cushion supported tracked vehicle whichemploys vertical and lateral acceleration sensor inputs to a computerwhich calculates the forces necessary to maintain the vehicle body on asmooth path and with banking on turns.

In the aforesaid copending parent application, Ser. No. 131,041, ofJames A. Ross there is disclosed a tracked vehicular transportationsystem employing polyphased linear motors both for suspension andpropulsion in which each motor is magnetically attracted upwardly by itsmagnetic field toward a support rail with a controlled air gapmaintained therebetween, and its suspension magnetic field is also usedto translate the motor and its supported vehicle along the track at aspeed related to the frequency of the polyphase alternating currentapplied to the motor.

Although any number of phases could be used, a three phase design isdisclosed because it is the simplest motor construction having thedesirable characteristic of providing nearly constant pole attraction asa function of phase rotation. The propulsion system is a variablereluctance, synchronous speed type wherein the rail is provided withrepetitive magnetic discontinuities (notches), or alternatively, thepropulsion system is a linear induction motor type wherein the rail isprovided with either a continuous conductive reaction strip or asquirrel cage winding (shorted rotor). Other disclosed.

propulsion systems are of the wound rotor and hysteresis types.

The terminal voltage applied to the polyphased motor windings to producethe attractive suspension force as well as the moving field forpropulsion is controlled by a non linear-feedback circuit which uses signals from displacement and inertial sensors carried on the vehicle formaintaining a selected air gap. The feedback is non linear in order tocompensate for the nonlinearity of the motor characteristic as afunction of gap length and of feedback operating frequency. Theattractive force produced by the magnetic field of the motor isproportional to the square of the motor current and inverselyproportional to the square of the gap length. The motor impedance,moreover, is resistive at zero frequency and largely inductive atfrequencies such as to 30 hertz which are relatively high for thefeedback apparatus.

The circuit elements of the feedback circuit provide the motor terminalvoltage in accordance with the following equation which expresses therelationship between the motor terminal voltage and the resultingattractive magnetic force produced between the motor and its supportrail:

E terminal voltage 1 air gap length f= frequency in hertz(cycles/second) K K constants F attractive magnetic force j= reactionsymbol.

In order to provide stable suspension of the vehicle, whether atstandstill or some propulsive speed, and at a selective gap which mayrange from substantially zero to one-half inches, the motor terminalvoltage E, whether d.c. at standstill or a.c. at the propulsive speed,produces an attractive magnetic force F which is opposite to thegravitational and inertial forces acting on the vehicle and sufficientto restore and maintain the same in stable suspension. The feedbackcircuit responds to signals from the displacement and inertial sensorsto produce various voltages indicative of these gravitational andinertial forces. For example, in a specific circuit arrangement, avoltage input of 4 volts to the square rooter element of the circuitindicates a gravitational force of l g which, of course, is the weightof the vehicle including its support motors. When this is the only forceon the vehicle, the magnetic attractive force F produced by the motorterminal voltage E is just sufficient to support the vehicle againstgravity at the selected gap.

Signals from the displacement and inertial sensors pass in parallelpaths through displacement and accelerometer channels in the inputportion of the feedback.

circuit. The displacement channel produces displacement signalsindicative of the length of the gap, velocity.

signals which are derived from differentiated displacement and areindicative of the rate of change of displacement, and change in loadingsignals which are derived from integrated displacement. The velocitysignals range in frequency from 1.2 to 5 hertz. The change in loadingsignals range in frequency from dc. to 1.2 hertz. The range offrequencies of maximum interest in the displacement channel thus extendsfrom dc. to 5 hertz.

Signals from the displacement channel are algebra ically summed withsignals from the accelerometer channel which has a frequency range ofmaximum interest extending from 0.3 to 30 hertz. Partial integration ofthe accelerometer feedback signal provides a quasi-velocity feedbackwhich is effective from a frequency of the order of 10 hertz down to 4hertz below which the differentiated displacement signal provides thevelocity feedback.

The square rooter element of the feedback circuit takes the square rootof the combined displacement and accelerometer channel signals toproduce a voltage corresponding to the equation quantity VT which isthereafter multiplied by the displacement function (IR) and thefrequency function 0K respectively, these equation functions beingperformed by mutliplier and amplifier-differentiator circuit elements.These circuit elements respectively provide d.c. and ac. paths for theirinputs, the dc path providing a voltage which increases with the gap andthe a.c. path providing a voltage which increases with increasingfeedback frequency, as is required to linearize the motor response withfrequency. The ac path includes a perfect differentiator which providesa first derivative of the input over a frequency range of fromessentially zero to 200 hertz.

The combined outputs of the multiplier and amplifier-differentiatorelements produce a unidirec' tional feedback voltage which representsthe equation quantity VF (lR jK w). The combined circuit gain requiredto produce suspension against gravity accounts for the constant K in theequation.

The varying frequency voltage required for propulsion at speeds upwardfrom zero is provided by a constant amplitude variable frequency threephase oscillator, the amplitude of each phase of which is increased as afunction of the frequency by an imperfect differentiator for each phaseto compensate for the increase in motor impedance due to the increase ininductive reactance with frequency. The differentiation is imperfect toassure an output at zero frequency and thus provide the magnetic fluxrequired in the motor-to-rail gap to establish suspension when thesystem is in operation at standstill.

The unidirectional variations of the feedback voltage are madeessentially to modulate the imperfect differentiator outputs for eachphase, it being a first input to each of three multipliers for the threephases, the other input for each of the multipliers being one of thedifferentiator outputs. Each of the multiplier outputs gives the productof the feedback voltage and the instantaneous value of each of thephased voltages in accordance with the three-phase variation thereof.

The output from each multiplier for each phase passes into acontrollable power supply having three outputs, one for each of thephased windings of the motor, the voltage output of each beingcontrolled accord ing to the variation of three phase electrical energywith time, including the special case of zero frequency wherein thephased outputs constitute frozen" instantaneous values which do not varywith time until a frequency variation is again produced to providepropulsion. Highly efficient controllable amplifiers of high powercapabilities such as the Class D type or thegated-silicon-controlled-rectifier type are employed to providepropulsive power for passenger-carrying railroad car type vehiclesweighing thousands of pounds.

An inertial or accelerometer type sensor which senses any accelerationin the vertical direction of the motor and its supported mass as thesame moves up and down in space is preferred since it provides signalsindicative of such movements without regard to the motor-rail spacialrelationship. Thus, the accelerometer sensor is not sensitive toirregularities in the track and does not pass them on to the passengersin the form of vibrations or jolts. On the other hand, the gain of thedisplacement channel is reduced as a function of gap change frequencyand only a mean gap is maintained by the displacement sensor. Analternative acceleration feedback sensor which senses relativeacceleration of the suspended mass with respect to the rail is suggestedfor use as a substitute for the inertial-reference accelerometer in thefeedback circuit when it is desired that the vehicle closely follow therail for technical reasons or to avoid the higher costs of the inertialaccelerometer. Hall-effect transducers which sense the flux in the airgap are suggested as a suitable sensor for such purpose.

The feedback loop that includes the inertial sensor makes a second ordercorrection to the overall feedback network of the order of db offeedback over the frequency of interest which is from 0.5 to 5 hertz.This makes the system insensitive to second order variations such aschanges in coil resistance with temperature and variations in the d.c.gain and ac. gain of the feedback network which may change from day today with weather changes, and for other reasons.

As aforementioned, the force exerted magnetically by the motor toprovide suspension varies as the square of the motor current andinversely as the square of the gap length. This is a non-linearrelation. However, the d.c. flux in the air gap remains the same fordifferent gap lengths when the current to gap ratio remains constant asit does, for example, when the current is doubled when the gap isdoubled, the magnetizing force or ampere turns per unit length of gapremaining the same. Non-linear elements in the feedback circuit, such asthe square-rooter circuit, linearize the voltage vs. force function forall gap lengths and thus allows the dynamic response of the feedbacksignals to be constant and provides constant stability for the system.The resultant linearization of the feedback circuit also providesconstant gain at all operating frequencies of the polyphase power andcorresponding propulsive speeds. This assures a smooth ride at allvehicle speeds. The smoothness of the ride, moreover, can be adjusted byadjustment of the feedback circuit, it being unnecessary to change themotor or any related parts of the structure.

The feedback circuit assures the stability of the vehicle with respectto the track, compensates for varying passenger loading and thrust dueto wind, and gradually corrects for unevenness of the track. Thefeedback circuit also inherently maintains lateral stability and anylateral perturbation is restored in a damped manner without overshoot.

SUMMARY OF THE lNVENTlON The present invention relates generally to thetransportation field and more particularly to a high speed trackedtransport vehicle which uses the same linear electric motors for bothsuspension and propulsion, such as disclosed in the aforesaid copendingparent application of James A. Ross, and which additionally may use suchmotors for vehicle guidance and banking.

The present invention follows the basic principles and incorporates thefundamental features of the parent application while providingimprovements in the composition and functioning of the non-linearfeedback circuit which controls both the magnitude and frequency of themotor terminal voltage to achieve suspension and propulsion at selectedpropulsion speeds, or suspension alone at standstill.

Specifically, the feedback control circuit of the present invention,while employing circuit elements for performing the multiplications andsummations of the voltage vs. force function equation:

as in the parent application, expresses this equation in the form where:

F is the attractive magnetic force E is the terminal voltage I is theair gap length R is the winding resistance f is the propulsion frequencyin hertz K K are constants j is the reaction symbol.

The square root function V? is developed from the sensor signal paths,as in the parent application. The multiplication of this function timesdisplacement and propulsion frequency, however, are performed in thepropulsion frequency control channel.

A first multiplier produces the product of the VT function times eachphase of a constant applitude three phase voltage of selected frequencywhich may be zero at standstill or a specific frequency corresponding toa desired propulsion speed. This product which represents K V? in theequation is the input to a second multiplier operating in parallel witha perfect differentiator. The second multiplier produces the product K 1VT IR and the differentiator produces the product K VI' K f, and theseproducts are summed and provided as the input to the three phasecontrollable power amplifiers which supply the terminal voltages to thethree phase motor windings.

This improved feedback circuit arrangement eliminates the imperfectdifferentiator of the parent application which increased the amplitudeof the oscillator signal, of each phase as the oscillator frequencyincreased. This required that the following multipliers be operated overan extremely wide dynamic range. A perfect differentiator which in thecircuit arrangement of the instant case provides the voltage vs.frequency function, follows the multipliers and thus permits the motorterminal voltage to be increased with frequency for any desiredpropulsion speed without exceeding the dynamic operating range of themultipliers.

The non-linear feedback circuit disclosed and claimed in the parentapplication is a species of the generic invention herein disclosed andclaimed wherein an electroresponsive force field generator and acoacting member separated or spaced therefrom are attracted toward eachother by the force field set up between them and are held separated fromeach other at a selected gap by an opposing force, it being the functionof the non-linear feedback circuit to so adjust the voltage of theelectroresponsive force field generator that the force produced by it isat all times sufficient relative to the opposing force to restore andmaintain stable equilibrium at the selected gap.

In the species of the invention disclosed and claimed in the parentapplication, the magnetic force field and feedback circuit arrangementsare made to be responsive to opposing force relationships wherein theopposing force is gravity and other acceleration forces tending to upsetthe stable equilibrium of the suspended vehicle and its support motors.

In the present invention, force field and feedback circuit arrangementsembodying the generic invention are also made to be responsive tolaterally directed displacement and acceleration forces on the vehiclesuch as may be caused by wind loads or may occur during turningmovements, to thus accomplish controlled magnetic guidance and bankingof the vehicle.

The foregoing and other features of the invention will become more fullyapparent from the following detailed description with reference to theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a schematic view of a forcefield generator embodying the voltage vs. force functions employed inthe present invention;

FIG. 2 is a schematic view of a tracked vehicle and its support motorsfor achieving magnetic suspension and banking in accordance with thefeedback principles of the present invention;

FIG. 3 is a schematic view of a tracked vehicle and its linear motorsfor achieving suspension and guidance of the vehicle;

FIG. 4 is a block diagram of a feedback control circuit for supplyingthe motor terminal voltages E and E of FIG. 2;

FIG. 4A is a schematic circuit diagram of one embodiment of the blockdiagram of FIG. 4;

FIG. 5 is a complete block diagram of the electrical system forachieving suspension and propulsion of a tracked vehicle and its linearelectric support motors;

FIGS. 6A and 6B, taken together, constitute a schematic circuit diagramof one embodiment of the block diagram of FIG. 5;

FIGS. 7A and 7B are graphs showing speed vs. frequency relationships forsynchronous relucatance and inductance motors respectively;

FIG. 8 is a plot of the open loop response of the system of FIGS. 6A and68 to a disturbing force; and

FIGS. 9 and 10 are graphs showing curves which represent thecharacteristic response of the system to load and track disturbances.

DETAILED DESCRIPTION Referring to FIG. 1, an electroresponsive forcegenerator M and a member R are separated physically by the air gapdistance or length l. Generator M and member R are mutually attractedtoward each other as indicated by the force field f set up therebetweenby generator M when a voltage E supplies a I thereto, the attractivcforce being designated F Assuming the member R to be fixed, that is,nonmovable, the force F is directed to depict that the generator M isattracted toward member R.

When the generator M, for example, is an electromagnet, or an electriclinear motor, and the member R, for example, is a ferromagnetic rail,the force F varies as the square of the current flowing in the windingof the electromagnetic device M and inversely as the square of the airgap length 1 between the device M and the rail R in accordance with theequation:

where:

A is the area of attraction in square centimeters N is the number ofturns in the winding of electromagnetic device M Equation (l) is derivedfrom two basic equations expressing magnetic circuit principles, onebeing that the magnetic force F between two parts of a magnetic circuitvaries as the product of their area of attraction A and the square ofthe magnetic flux density B at their interface:

F =AB /(81r X 981) where:

B is the flux density in gauss F is the force in grams and the secondprinciple being that the magnetizing force H required to set up a fluxin an air gap 1 between the parts is equal to the flux density 8:

where:

NIH is ampere turns per centimeter l is air gap length in centimeters Bis flux density in gauss Combining equations (1 and (1 F [A/(81r X 981)](Mr-NI/IOI) [A/(81r X 981)] (41rN/IO) (I/l) l /l) 1( (1) It will benoted that the magnetic force F is the same for any air gap within awide range of air gaps as long as the ampere turns per unit length orthe air gap, namely, the ratio NIH, is constant. Thus, for example, theattractive force will remain the same if the current is doubled when thegap length is doubled.

The linear relationship between the current and gap length is apparentfrom a re-write of equation (1):

V FMD/ V 1 where the current varies directly with the air gap and as thesquare root of the force F The current varies directly as the voltage Eacross the winding of the electromagnetic device M and can be changed bychanging the voltage:

where:

R jmL is the winding impedance R is the winding resistance L is thewinding inductance j is the reactive symbol to is Zarf fis frequency inhertz (cps) E is the voltage across the impedance. Combining equations(1,) and (2):

=l( VFM 1) +j The inductance of an electromagnetic device M separatedfrom a ferromagnetic member R in a magnetic circuit the therewith havingan air gap 1 therebetween varies inversely as the length of the air gap:

Combining equations (2,) and (3):

E= K, VTJ R K,,jw)

E=K3 VT IIIHX, VFJK w In order to keep equation (4,) in balance, anychanges in F,,,, and/or in l in magnitude and rate must be accompaniedby a change in E, and any such changes in E must be both in magnitudeand rate of change, the latter giving rise to a frequency component inE, and this, in turn, causing the reactive voltage component K V F M Kjw to increase directly in proportion to the increase in the frequency.The voltage E, of course, must increase, as required, to compensate forthe increase in the winding impedance due to the increase in inductivereactance with frequency. At zero, or very low frequencies, the windingimpedance is substantially resistive, and the voltage E is substantiallyequal to the resistive voltage component K VFMIR, the voltage E in suchcase being characterized only by its magnitude, being essentially d.c.

Referring again to FIG. I; assume that an opposing force F is acting onthe force generator M in a direction opposite to the attractive force FIf the attractive force F,, is made to equal the opposing force F theseparation distance I will be constant and the generator mass M will bein a state of stable equilibrium.

In the aforesaid parent application Ser. No. 131,041, a tracked, highspeed vehicle is disclosed having four linear electric motors mounted atthe four corners thereof for suspension and propulsion of the vehiclefrom and along the track by magnetic attraction. This arrangement isdisclosed, in part, in FIG. 2, wherein the rear motors M, and M, areshown in spaced dependent relation to their respective support rails R,and R being separated therefrom by the air gaps l, and 1 The rails aresupported in fixed relation on the track generally designated T.

The vehicle V which moves along the track T is supported by and securedto the front and rear motors of which the rear motors M, and M, areshown secured to the vehicle as by the mounting brackets schematicallydesignated 12, and b The magnetic attractive forces F and F,respectively of the motors M, and M, are opposed by the forces F and FThese opposing forces may be considered generally to be accelerationforces expressed by the equation:

F= Ma where:

F is the acceleration force M is the mass of the body acted upon by theforce F a is the acceleration of the body represent W When the air gapsl, and I are static, there being no change in the gaps, thecorresponding forces F and F represent the weights supportedrespectively by the magnetic forces F and F of motors M, and M Weight Wis the force which gravitation exerts upon a body and is equal to themass of the body times-the local acceleration of gravity g, thus:

F=Ma

as before set forth in equation (5). Now with g substituted for a, and Wsubstituted for F:

W Mg

and

M W/g Motors M, and M by their attractive forces F and F support theirown weights W and W and one fourth the weight Wv/4of the vehicle, thus:

Vehicle V carries a pair of position or placement sensors S and S whichrespectively sense the length of the air gaps l, and 1 associated withmotors M, and M Signals from these sensors operate in their respectivefeedback circuits, subsequently to be described, to produce voltagestherein which represent the attractive forces F and F required toproduce the voltages E, and E: for support of the motors M, and M atselected gaps l, and I such representative voltages corresponding to thevoltage component F of equation (4).

When it is desired to maintain constant motor gaps notwithstandingchanges in passenger loading, or, wind loading, on the vehicle, suchchanges will, in turn, change the opposing forces and the gaps. Theposition sensors, however, sense the gap changes and produces signalswhich are integrated to produce appropriate adjustment in the feedbackvoltages representing the forces F and F These signals, moreover, aredifferentiated to provide velocity feedback for dampening adjustment ofthese voltages.

Vehicle V further carries accelerometer sensors S and 8, which are madeto sense up and down accelerations of the vehicle caused, for example,by variations in the vertical radius of curvature of the track to thusproduce signals for the further adjustment of the feedback voltagesrepresenting the magnetic forces F and F and, further, by theintegration of such signals, to develop velocity feedback voltages forthe development of the reactive voltage component of equation (4).

A second pair of accelerometers S and 8 are carried on the vehicle anddirected to sense lateral accel erations occuring during turningmovements of the vehicle so that signals therefrom may be used toproduce relative adjustments of the gaps l and I for banking purposes,thereby obviating the need for banking the track and rails R and R Thus,for example, referring again to FIG. 2, and assuming that the vehicle Vis caused to move in a turn to the left, the sensors S and S will senseacceleration forces directed to the right of the vehicle, and signalsfrom sensor S associated with motor M will cause a decrease in gap 1 andsensor S associated with motor M will cause an increase in gap 1 therebyto effect the desired banking to negotiate the left turn.

Referring now to FIG. 3, there is shown thereon a vehicle V having threelinear electric motors M M and M of which M is used for suspension andpropulsion, or for suspension alone, and motors M and M are used forguidance and propulsion, or for guidance alone. Their respective forcefields are designated f ,f and f and are generated in relation to theirassociated fixed rails R R and R in the same manner as the force fieldsfand f of motors M and M of FIG. 2.

The gaps l and will normally be equal so that the magnetic attractiveforces F and F will also be equal and, being opposite, will present therequired opposing force, each to the other, to maintain balance. In thiscase, the attractive forces, at equal gap lengths 1 1 may be set at anydesired strength upwards from zero. At zero force setting, of course,there would be no force fieldsfl and f Considering first the zero forcefield setting at equal gaps, it will be presumed that provision is made,as subsequently described, for producing either of the forces F and P asits associated motor M M is moved with the vehicle to increase its gap 1or 1 above the equal gap setting In such case, the generated attractiveforce will setting. in proportion to the increase in gap and will opposethe acceleration force on the vehicle which caused the particular gap1., or I to increase. In this case, one of the accelerometer sensors Sor S will aid in the development of the attractive force required toovercome the lateral acceleration force. When the acceleration ceases,the other sensor will generate an opposing attractive force to controlthe deceleration of the vehicle upon return of the same to the equal gapcondition.

When it is desired to use the force fieldsf, and f., for propulsion, inaddition to guidance, some suitable strength of opposing attractiveforces F and F is maintained at all times.

The feedback circuits of FIGS. 4 and 4A are taken from the parentapplication and are incorporated in this disclosure as embodiments ofsuitable circuitry for developing the magnetic attractive forces F to Fof FIGS. 1 to 3, the feedback circuits for this purpose performing themultiplications and summations of equation (4). Other disclosures of theparent application are incorporated herein by reference to thatapplication.

Referring first to FIG. 4, the accelerometer 20 represents any of theaccelerometer sensors S and S of FIG. 2 and S of FIG. 3 which have amass of relatively appreciable magnitude disposed to be sensitive tovertical accelerations. It also represents either of accelerometersensors S and S as the same are employed in the FIG. 2 and FIG. 3arrangements to sense lateral acceleration and thereby provide inputs tothe feedback circuits of motors M and M and motors M and M respectively,in the same manner as sensors S and S provide inputs to their respectivefeedback circuits.

Accelerometer 20 may be of a piezoelectric type, such as Endevco type2200, or a servo type such as developed for space use which does nothave the very low frequency noise and random variations characteristicof the piezoelectric types.

Signals from accelerometer 20 pass through a compensating network 21which alters the frequency vs. amplitude response thereof to provideabout 10 db of feedback within the range of frequencies of the order ofh to 5 hertz to make the suspension system insensitive to second ordervariations such as variations in motor magnetic structure, variations inthe a.c. resistance of windings, winding resistance variations withtemperature, d.c. and a.c. gain variations in the feedback network, andinstability at certain gap lengths. Network 21 also integrates theaccelerometer signals to provide velocity feedback which is effectiveover a range of frequencies of the order of 4 to 10 hertz.

Position transducer 22 is a sensor element which provides length of gapinformation and represents any of the length of gap sensing position orplacement sensors S to S of FIGS. 2 and 3. Sensor element 22 may employmechanical contact, or optical, sonic or other suitable means toaccomplish measurement of the gap which may range from substantiallyzero to one-half inchesv Position transducer 22, for example, may be alinear potentiometer having a mechanical roller which is carried by itsslider and urged yieldably into contact with rail 2 whereby thepotentiometer is adjusted as the roller and slider are moved in responseto any changes in the motor-to-rail gap as the roller rides along therail. Motor 1 and rail 2 represent the various motor and railcombinations disclosed in FIGS. 2 and 3, and the potentiometer may besuitable carried either by the vehicle or on the particular motor withwhich it is used.

An optical displacement sensor 22 may be arranged with a photocell onone side of the motor-rail gap and illumination means on the other sothat more or less light is caused to enter the photocell to change itselectrical response as a function of gap length.

An ultra-sonic sensor 22 may be arranged to produce ultra-sonic soundreflections from the rail so that detected changes in phase of thetransmitted and reflected sound may provide a suitable measure of gaplength and changes therein.

Signals from position transducer 22 are supplied to a compensatingnetwork 23 and also to a multiplier 25, subsequently to be described.

Compensating network 23 provides an adjustable reference for the gapmeasurement in electrical terms, that is to say, this reference may beadjusted to preset a selected gap which the position sensor will seek.The compensating network 23 also has provision for adjusting itsposition signal to zero for a selected gap, or to some strength otherthan its normal signal for that gap for purposes of the FIG. 3 vehicleguidance operation, aforedescribed. The compensating network 23,moreover, has provision for receiving signals from the accelerometersensors S and S of FIG. 2 to provide banking adjustment of gaps l and 1as aforedescribed. Network 23, in addition, provides velocity andintegrated displacement feedback. Integration is performed over a rangeof frequencies from to about 1.2 hertz, and differentiation is performedover a range of frequencies from 1.2 to about 5 hertz.

Signals from the compensating network 23 pass to compensating network 21where they are combined, that is, are algebraically summed with theacceleration signals for common amplification to provide aforceproportional voltage representative of the function F in equation(4). This force-proportional voltage operates in the whole feedbacksystem to enable motor 1 to produce a magnetic force P of l g, that is,an equal and opposite force in relation to gravity whereby themotor-vehicle mass is magnetically suspended.

As hereinbefore discussed, the magnetic force F is proportional to thesquare of the motor current which is a non-linear relationship whichmust be linearized in order to provide feedback stability. Linearizationis achieved by taking the square root of the forceproportional voltageoutput of network 21 in accordance with the mathematical requirementexpressed by the function V F in equation (4).

This required square-rooting of the forceproportional voltage output ofnetwork 21 is performed by the square-root circuit 24 which is typicallyan operational amplifier entity employing non-linear transistorcharacteristics to give an electrical output that is the equivalent ofthe square-root of the electrical input.

The length of gap and square-root outputs of position transducer 22 andsquare-root circuit 24 are applied as first and second inputs tomultiplier 25 and multiplied thereby to provide a product whichcorresponds to the product requirement VT"; X lR of equation (4).Multiplier 25 is an operational entity whose output is the product oftwo electrical inputs, and it thus provides an output voltage thatincreases with gap length. The electrical path through'multiplier 25 isindependent of frequency so that an output is produced thereby at zerofrequency which is the condition when the gap length is constant betweenthe motor 1 and rail 2.

The output of square-root circuit 24 is also applied to perfectdifferentiator 26 which is an amplifier having a resistance-capacitancecircuit to perform electrical differentiation and thus provide the firstderivative of its input over a frequency from substantially zero to 200hertz. The capacitor is not shunted by any conductive path and so theoutput of the differentiator is zero for zero frequency, that is, ford.c., which is the condition when the motor-to-rail gap is constant. Theamplifier-differentiator circuit of perfect differentiator thus producesand provides an ac. path for the voltage which represents the reactivecomponentj VHX K w of equation (4). The output of differentiator 26 thusprovides a voltage which increases with the feedback frequency, that is,the frequency of the sensed signals.

The outputs from multiplier 25 and differentiator 26 are summedalgebraically to provide to the input of amplifier a feedback controlvoltage which represents the sum of the resistance and reactance voltagecomponents of equation (4), namely,

After amplification at level raising amplifier 95, and gain settingpotentiometer 96, the feedback control voltage is applied to thecontrollable power supply 38 which is a power amplifier of the Class Btype for low power output of about one kilowatt or of the Class D typeor gated-silicon-controlled-rectifier type for higher power outputs. Thebasic source of power for these amplifiers, for example, is an externalpower supply 39 having 3rd rail connections 39' with the vehicle V.

Controllable power supply 38 provides the terminal voltage E applied tomotor 1 to develop the magnetic attraction force F The combined gains ofpotentiometer 96 and the voltage gain of amplifier 38 determines theconstant K in equation (4) such that the motor terminal voltagesbecomes:

which is equation (4).

The motors may be built in a large range of sizes, but as an example,for a 30 inch long motor capable of supporting 2,000 pounds, the severalaforementioned constants may have values expressed in inches as follows:

Referring now to FlG. 4A, accelerometer 20 is a piezoelectricaccelerometer of the Endevco type 2200 and is shown to have a mass 40 ofappreciable magnitude which is so disposed on the vehicle V or on motor1 of FIG. 4 so as to be sensitive to vertical acceleration to thusenable the accelerometer to perform its required feedback functions, asaforedescribed, as well as to provide the soft ride features whichcharacterize this invention.

Amplifier entities 41, 42 and 43 comprise elements of compensatingnetwork 21.

Amplifier 41 is a known impedance-matching amplifier and is required toreduce the very high impedance of a piezoelectric accelerometer to anordinary circuit value. The amplifier is a Motorola MC l456G integratedcircuit amplifier, or an equivalent operational amplifier. It isconnected as a source-follower and has no gain, nor phase shift. Theinput circuit includes resistor 44, of 250 megohms resistance, connectedfrom amplifier terminal 3 to ground to provide an input bias currentpath for the amplifier. This is shunted by capacitor 45, of 1,000picofarads (pf) capacitance, which acts as a padding capacitor to thestray capacitance of the input lead from the accelerometer to terminal3. The several terminals of the integrated circuits, operationalamplifiers, etc. have been given small numerals, corresponding to thosegiven by the manufacturer on the device itself. The internal circuitsfor these devices are known from the manufacturers catalogs.

Amplifier 41 has a feedback circuit between its terminals 6 and 2comprised of a 250 megohm resistor 46, shunted by capacitor 47, of 1,000pf capacitance. Terminal 7 is connected to a direct current energizingpower source having a voltage of the order of 15 volts, while terminal 4is connected to a similar source having the opposite polarity of- 15volts. Each of these connections is filtered by a 0.1 microfarad (pf)capacitor connected therefrom to ground.

Capacitor 48, of 200 uf capacitance, is connected to the output terminal6 of amplifier 41 to restrict the low frequency signal amplitude fromthe accelerometer with a roll-off starting at 0.13 hertz. This removesthe noise" from the accelerometer circuit at low frequencies. Resistor49, of 6,800 ohms, connected in series with capacitor 48 and withresistor 50, of 0.2 megohms, sets the accelerometer channel gain.Amplifier 42 provides an accelerometer channel gain of 200/6.8 30. Thesecond terminal of resistor 49 connects to input terminal 2 of amplifier42, a Motorola MC 1741CG integrated circuit or equivalent.

There is also another connection to terminal 2; from the output of thegap-length sensor circuit, to be later described.

Amplifier 42 functions as a simple amplifier, having a feedback circuitconnected between input terminal 2 and output terminal 6 comprised ofresistor 50, of K ohms, shunted by capacitor 51, of 1,500 pf. Thevoltage supply and grounding connections are standard and are known. Thegain of amplifier 42 is approximately 30, up to an upper cut-offfrequency of 8 hertz.

The algebraically summed signals from the accelerometer and gap-sensornow pass into terminal 2 of amplifier 43, of MC 1741G type, throughresistor 53, of 30,000 ohms resistance, which is used for gain setting.The feedback circuit of amplifier 43 is the same as that of amplifier42; i.e., resistor 50 of 0.2 megohm and capacitor 55 of 0.2 microfarad.Supply circuits are conventional. The gain of amplifier 43 isapproximately 7, with an upper cut-off frequency of 4 hertz.

Capacitor 55 acts as a partial integrator upon the acceleration feedbacksignal. This provides a quasivelocity feedback signal and prevents anoscillatory condition otherwise existing because of an 180 phase shiftbetween acceleration and displacement. This is effective from afrequency of the order of 10 hertz down to 4 hertz. Below 4 hertzdifferentiation of the position (displacement) feedback occurs toprovide the velocity component. This is produced by capacitor 58 in theinput circuit to amplifier 61, hereinafter to be described.

The combination of these two signals gives control of the phase of thefeedback circuit so that displacement information can be fed into asystem that has feedback from an accelerometer included in it. Actually,four aspects of feedback are present in the system to give a high degreeof stability; the integral of displacement to bring the system back to amean gap length after load changes in the vehicle, displacement feedbackto stabilize the integral displacement feedback circuit, velocityfeedback to stabilize and damp the displacement feedback, andacceleration feedback to stabilize and damp the velocity feedback. Atthe same time the acceleration feedback corrects second ordernon-linearities in the linearizing circuit comprised of square-rootcircuit 24, multiplier 25, and differentiator 26. This mode of operationis required for any system of the nature of a magnetically supportedrailroad, where the air-gap length is purposely allowed to vary toaccommodate rough track." The gap is brought back to a mean valuegradually, to provide a soft" ride.

Position transducer 22 is shown to be a potentiometer 56 connected toground and shunted by a source of voltage such as battery 57. Its slideror wiper carries the aforedescribed rail-engaging-roller, not shown.Typically, battery 57 may have a voltage of 10 volts and the travel ofthe slider have a travel of one-half inch. This range of travel normallycovers the operating change in the length of the air gap, the preferredlength of which is one-quarter inch or perhaps slightly less. Theseconstants give a voltage of 20 times I; i.e., 20 times the length of theair gap as measured in inches. Battery 57 may, alternately, be aregulated power supply of the same voltage.

The output from position transducer element 22 passes to compensatingnetwork 23. Capacitor 58, of 0.1 pf, in series with resistor 59, of4,700 ohms, all shunted by resistor 60, of 1.5 megohms, are the initialelements of compensating network 23. This network has a resistiveimpedance of 1.5 megohms from d.c. to 1.2 hertz, decreasing to about4,700 ohms at 350 hertz. This provides a velocity signal (i.e.,differentiated displacement) at frequencies above 1.2 hertz.

This output passes to input terminal 2 of operational amplifier 61, anMC 1741G type. Both input terminals 2 and 3 of this amplifier areindividually returned to ground through resistors 62 and 63, of 22,000ohms, to provide a path for the input bias currents of this amplifier.

The feedback circuit for amplifier 61 is comprised of resistor 64,10,000 ohms, in series with capacitor 65, uf; with resistor 66, 100,000ohms, shunted across the capacitor. This gives an impedance of 110,000ohms for d.c. and of 10,100 ohms at 14 hertz, approximately. Thisresults in the gain of amplifier 61 at frequencies below 1 hertz beingconsiderably greater than at higher frequencies. This is to increase theloop gain at low frequencies and to provide an integral of displacementfunction as a feedback signal to gradually correct for changes in load.

Since the purpose of the feedback system is to correct for changes inloading of the vehicle, wind pressure and unevenness of the track, thefrequency of the feedback signals is very low with respect to thefrequencies handled by usual electrical networks. Feedback must bemaintained at zero frequency (d.c.). The range of frequencies of maximuminterest extends from 0 to 5 hertz for the displacement channel and from0.3 to 30 hertz for the accelerometer channel.

Potentiometer 67, of 50,000 ohms total resistance, is connected betweenpositive and negative voltage supply sources, each of which has avoltage of 15 volts with respect to ground. Bypass capacitors, of 50 at,are provided from each to ground to remove extraneous variations, asknown. Potentiometer 67 provides a voltage adjustment for any initialoffset voltage in amplifier 61. Its slider is connected to inputterminal 3 thereof, through isolating resistor 67 of 1 megohm.

An additional input to terminal 3 of amplifier 61 is from potentiometer68, of 2,000 ohms, and passes through attenuating resistor 68' of 1.5megohms, to provide a reference displacement proportional voltage.

Amplifier 61 generates an output voltage proportional to the differencebetween the voltage reference input to resistor 68' and the input toresistor 60, which is the voltage from displacement transducer 22.Voltage dropping resistor 69, connected in series with potentiometer 68from the positive voltage connection to ground, typically has aresistance value half as great as the resistance value of potentiometer68.

The output of amplifier 61, from terminal 6, passes to terminal 2 inputof amplifier 42 through resistor 66', of 22,000 ohms, a summingresistor. It is at this point that compensating network 23 joins that of21, for the inclusion of amplifiers 42 and 43 in common. The output fromamplifier 43 is taken from terminal 6 and passes through diode 54 withthe cathode thereof connected to the terminal so that only negativesignal variations will be passed on. Additionally, diode 52 is connectedas a feedback element on amplifier 43 to prevent positive voltageexcursions.

Only negative voltages are allowable at the input of the square-rootcircuit which follows because inversion therein to positive signalpolarity occurs before the square-root function takes place. Thisprevents taking the square-root of negative numbers, which areimaginary. Herein the square-root circuit becomes inoperative becausefeedback of positive polarity drives it to current saturation.

The force-proportional voltage output at amplifier 43 is made to belinearly proportional to a force between the load mass and the rail.Referring to equation (4), to develop the proper voltage E to be appliedto the motor windings, the force-proportional voltage is to besquare-rooted and multiplied by (IR +jK.,w).

The first electrical device to significantly execute the mathematics oflinearization is the square-root circuit 24. This may be an integratedcircuit 24', of type MC 1494L (Motorola) normally known as a multiplierof electrical signals fed into it. This multiplier is placed in thefeedback circuit of an operational amplifier 70 and the square-root ofthe signal input is provided therefrom. The theory and practice of thissquare-root performance is known, being set forth in the (Motorola)manufacturers, Specifications and Applications Information, October 1970DS 9163. Operational amplifier 70 may be an MC1741G integrated circuit.

The output from the previously mentioned diode 54 is connected togain-setting resistor 71, of 52,000 ohms, and also to ground throughresistor 72, of 1,000 ohms. The latter resistor provides a path for anyleakage current in diode 54. The input from resistor 71 is connected toterminal 14 of multiplier 24' and also to terminal 2 of amplifier 70.The output of this amplifier, at terminal 6, is connected to terminals 9and 10 of the multiplier and also to ground by a small capacitor 73, of10 pf capacitance, in series with resistor 74, of 510 ohms. Zener diode75 is also connected between the output of amplifier 70 and ground toprevent accidental latch-up (malfunctioning) of the circuit. A type1N524l may be used.

The feedback path for amplifier 70 is the multiplier 24' connectedbetween input terminal 2 and output terminal 6 of amplifier 70 andterminals 9 l and 14 of the multiplier. Capacitor 76, of pf capacitance,is connected between amplifier terminals 2 and 6 for the purpose ofphase-compensating the amplifier. Input terminal 3 thereof is connectedto the slider of potentiometer 77, which potentiometer has a resistanceof 20,000 ohms. This provides a voltage reference for the amplifier.This potentiometer is connected in parallel with a duplicatepotentiometer 78, which is connected between terminals 2 and 4 ofmultiplier 24'. A resistor 79, of 62,000 ohms, and a resistor 80, of30,000 ohms, are respectively connected between terminals 7 and 8 and 11and 12 of multiplier 24'; and a resistor 81, of 16,000 ohms, isconnected between terminal 1 and ground. A voltage source, typically of15 volts of positive polarity, is connected respectively to terminals 7and 15 of the amplifier and multiplier, whereas a voltage sourcetypically of 15 volts of negative polarity, is respectively connected toterminals 4 and 5 of the amplifier and multiplier.

At the input to the square-root circuit 24, a negative signal voltage of4 volts produces in the whole system a force of l g; that is, there isproduced an equal an opposite force in relation to that of gravity,whereby the motor-vehicle mass is magnetically suspended. With theconnections and voltages given, the output of the square-rooter circuit24 at terminal 6 of amplifier is the square-root of 10 times the input.This is the square-root of 10 in efiective amount and is taken intoconsideration in establishing the whole feedback gain. Mathematically,such functioning of the electrical circuits is accounted for in thevalues of the several K constants.

The output from the square-root circuit is connected to the input ofmultiplier 25 to perform the IR portion of equation (4), and also to theinput of perfect differentiator 26 to perform the jK w term. The inputto multiplier 25 is terminal 10 of multiplier 25' and to the perfectdifferentiator is capacitor 83 through resistor 90.

The above input to the multiplier may be termined the x input. The yinput is connected to input terminal 9 and comes directly frompotentiometer 56 of position sensor 22 through resistor 84 forisolation. The resistance value of resistor 84 may be 0.1 megohm. Bothinput terminals 10 and 09 are also connected to ground throughcapacitors 85 and 85, of 10 pf capacitance, in series with resistors 86and 86, of 510 ohms resistance, respectively. These prevent highfrequency parasitic oscillations.

Resistors 79, and 81 are identical in resistance value and connection tomultiplier unit 25 as these were with respect to unit 24 of square-rootcircuit 24. So also are potentiometers 77' and 78', except that theresistance value of potentiometer 77 is 50,000 ohms. An additionalpotentiometer 87, of 20,000 ohms, is connected across terminals 2 and 4of units 25', with the slider connected to terminal 6. These threepotentiometers are adjusted to give proper x, y and output offset bias,as outlined in the manufacturers Specification and ApplicationInformation previously referred to.

An MC 1741G operational amplifier 89 coacts with multiplier unit 25' togive the complete multiplier 25. Feedback capacitor 76', of 10 pf, isconnected to the amplifier at terminals 2 and 6, and is shunted byresistor 88, of 52,000 ohms. Positive and negative voltage supplysources are as previously described.

Perfect differentiator capacitor 83 has a capacitance of 0.2 pf. It isin series with resistor 90, of 1,000 ohms resistance. The capacitorconnects to input terminal 2 of operational amplifier 91, which may be aMC 17416 type. The feedback circuit of this amplifier is comprised ofcapacitor 92, of 0.0068 at, and resistor 93, of

0.1 megohm, in parallel and connected between amplifier terminals 2 and6. Second input terminal 3 is grounded. Positive power supply voltage isconnected to terminal 7, while the same in negative polarity isconnected to terminal 4. This amplifier-differentiator provides thefirst derivative of the input over a frequency range of from essentiallyzero to 200 hertz.

The output from amplifier 91 is taken through summing resistor 94, of62,000 ohms, to input terminal 2 of amplifier 95. The latter mainlyraises the signal level, after providing for the summing, for parallelfeeding all of the three-phase multipliers that follow. Similarly, theoutput from multiplier operational amplifier 89 is taken through summingresistor 94, of 62,000 ohms, and connects to input terminal 2 ofamplifier 95. This provides the total electrical representation of FURjK w) of equation (4).

The feedback circuit 92', 93 of amplifier 95 is the same as the feedbackcircuit 92, 93 of amplifier 91; also, input terminal 3 is connected toground and the power supply connections are the same as for amplifier91.

The output at terminal 6 of amplifier 95 passes to potentiometer 96,which is grounded, as shown. The slider of the potentiometer isconnected to the controllable power amplifier 38 of FIG. 4 whichprovides a motor terminal voltage and motor current which, in turn,produces a magnetic force F equal to 1 g when a negative voltage inputto the square root circuit is 4 volts.

Considering operative details of the feedback circuits of FIGS. 4 and 4Awhich are designed to provide a smooth ride in the transportation ofpeople, adjustment of the suspension gap length l is accomplished byvarying the voltage at input 3 of amplifier 61, as determined by thesetting of potentiometer 68. The gain of amplifier 41, of course, isunity. The gain of amplifier 42 is approximately 30, up to an uppercut-off frequency of 8 hertz. The gain of amplifier 43 is approximately7, with an upper cut-off frequency of 4 hertz. When the output of thisamplifier is -4 volts, the force exerted by motor 1 is l g; i.e., thevehicle is suspended.

In forming the feedback circuits according to this invention use is madeof the fact that the ac. flux density in the motor to rail air-gap doesnot vary if the length of the gap changes. This flux density is affectedonly by the value of the volts-per-turn in the magnetic structure, andso the voltage only in any given magnetic structure. Multiplier 25provides compensation for d.c. flux density changes with change in thelength of the aingap. Position transducer element 22 senses the dc gaplength and the gain of the feedback circuit is modulated to increasewith gap length, maintaining the overall system gain, including thecharacteristics of motor 1, constant.

In a typical motor the inductive reactance of the coils is equal to theresistance of the coils at a frequency of the order of 2 hertz. Theinductance varies inversely with the length of the air-gap. Properfeedback performance is maintained, however, by provision of the dc.path through multiplier 25 and the ac. path through perfectdifferentiator 26. The exciting current through the motor coilsincreases with gap length, thus the dc. flux remains constant.

In practical operation, this necessary mode of operation requires thatextended periods of suspension at long air-gaps cannot be allowed. It isgood practice to rate the amplifiers comprising controlled power supply38 for the average length of gap encountered and to return the vehicleto that length within a few seconds without causing an artificial joltafter a gap-lengthening perturbation.

The force exerted magnetically by the motor in providing suspensionvaries as the square of the current in the windings of the motor. Thisis a non-linear relation. Non-linear elements in the feedback circuit,such as the square-root circuit 24 of FIGS. 4 and 4A make the output ofthe feedback circuit linear, from a voltage input to a force output.This results in a constant feedback loop gain at all values ofalternating current frequency and at all gap lengths of the motor to therail. Moreover, this results in a uniform easiness of ride. A typicalvariation of gap may extend from percent to nearly 100 percent of anormal value of 1.0 inch. To prevent the motor from actually contactingthe rail, a flat automotive type brake shoe may be arranged to bear uponthe rail instead, as a safety measure.

Because an inertial reference, accelerometer 20, is used in the verticalplane, the feedback circuit ignores small track irregularities and doesnot pass them on to the passengers in the form of vibration or quickjolts. Only a mean gap is maintained by the displacement (position)transducer 22.

Referring again to the FIG. 4A showing of compensating network 23, aselected gap 1 for suspension would normally be set by adjustment ofpotentiometer 68. If the same magnetic forces involved in suspension areapplied laterally as in FIG. 3, and the motors M M therein have selectedgaps which are equal, the magnetic forces F and F will be equal andopposite and each have a magnitude corresponding to their equal gapsdetermined by adjustment of their respective potentiometers 68. When itis desired that the forces F and F be generated only upon deviationsfrom the equal gaps, offset voltage adjusting potentiometer 67 is set toreduce the voltage applied to input terminal of amplifier 61 to zero.

When it is desired that some magnetic coupling between the rails R, andR and motors M, and M be maintained at all times, as for increasedstability in guidance control notwithstanding the accompanying magnetidrag, or to provide propulsion, the potentiometers 67 for the respectivemotors may be set at some suitable value to provide strengths F and Fwhich are greater than zero at equal gap settings.

For purposes of achieving banking of the vehicle V shown in FIG. 2,banking control channels for accelerometer sensors S and S respectivelycomprise its accelerometer and an amplifier such as amplifier 41together with its associated input and output circuit elements. In suchcase, the output resistor 49 of each banking control channel isconnected as shown in FIG. 4A to the slider of potentiometer 67. Anyinput from the banking channel will thus alter the gap as long as thelateral turning force sensed by its accelerometer persists.

Reference is now directed to FIGS. 5 and 6 which disclose the preferredembodiment of a complete feed back circuit for controlling both thesuspension and propulsion of a tracked vehicle-linear electric motorsystem such as disclosed in FIG. 2.

Referring first to FIGS. 5 and 2, the accelerometer 20, as before,provides a signal proportional to an upward or downward inertial forceacting on the vehicle V. The position transducer 22, as before, providesa signal proportional to the length of the motor-torail gap 1.

The frequency compensating networks 21' and 23' have generally the samecomposition as their counterpart circuit networks 21 and 23, of FIG. 4,and function, moreover, generally in the same manner to produce at theoutput of network 21 a force-proportional voltage which represents thequantity F in equation 4). When this voltage is a negative 4 volts, theterminal voltage at the motor windings is just sufficient so that themotor produces a suspension force F of lg.

Square root circuit 24" also has generally the same composition andfunctions generally in the same manner as its counterpart-element 24 inFIG. 4 whereby the square root of the force-proportional voltagerepresented by V F in equation (4) is provided in its output.

For the purposes of explaining the feedback circuit arrangement of FIG.and its manner of functioning to perform the summations andmultiplications required by equation (4), this equation preferably isexpressed in the form:

where:

j represents the reaction symbol f is the propulsion frequency K and Khave constant values hereinafter to be described.

The multiplications and product summations involving the square-rootquantity mas set forth in equation (9) are performed in a frequencycontrol channel presently to be described. This channel comprises speedcontrol 30, three phase variable frequency oscillator 31, multipliers120 to 122 and 135 to 137, and differentiators 143 to 145.

Speed control 30 controls the frequency of oscillator 31 whichpreferably provides the three phase voltages A, (b3 and C, although anynumber of phases from two upward may be used. The three phases typicallyare separated by 120 electrical degrees in time, and the circuits andwindings 111, 112 and 113, FIG. 6B, are typically star (i.e., Y)connected. Oscillator 31 supplies alternating current at constantamplitude and essentially of sinusoidal shape over a frequency rangefrom zero frequency at standstill to a low audio frequency of the orderof 80 hertz at high speed.

When the system is in operation at standstill and zero frequency, eachphase of the oscillator is required to produce an output to enable thefeedback circuit to provide the suspension magnetic flux in themotor-torail gap. It will be understood, however, that the system may beoperated at standstill at any frequency providing at least one of thethree phase windings is disconnected so that the moving field requiredfor propulsion is not established, and at least one of the phasedcircuits is in operation to enable the feedback circuit to develop thesuspension flux.

Oscillator 31 may be comprised of three mechanically drivensine-wave-generating potentiometers to provide relatively lowfrequencies, the potentiometers being rotated by hand for testing or bya geared-down variable speed motor for relatively low speed transportuse. In such case, speed control 30 is a rotatable shaft, hand or motordriven, having three potentiometer sliders attached thereto andangularly spaced apart from each other thereon by electrical degrees.The potentiometers are of circular configuration and suitable for fulland repeated rotation of the sliders thereon. The potentiometerspreferably are wound to provide sinusoidal voltage variations withrotation of the sliders, the three phase output being provided therefromwhen a dc. source is applied across the potentiometers connectedelectrically in parallel.

Oscillator 31, alternatively, may be a function generator such as type120-020-3, manufactured by the Wavetek company of San Diego, Calif. Suchoscillators are voltage responsive, the frequency output increasing withthe input voltage. In such case the speed control device 30 may be apotentiometer.

The three phase output from oscillator 31, namely, phased voltages (11A,B & 42C, are applied as the X inputs to multipliers 120, 121 and 122,respectively, the aforementioned square root voltage from the squarerootcircuit 24" being applied to the Y inputs thereof. The resulting productoutput of each of these multipliers is a sinusoidal voltage having amagnitude represented by the equation product K VF The outputs frommultipliers 120, 121 and 122 are applied, respectively, as the X inputsto multipliers 135, 136 and 137, the aforementioned air gap lengthproportional signal from transducer 22 being applied to the Y inputsthereof. The resulting product output of these multipliers is asinusoidal voltage having a magnitude represented by the equationproduct K VHIR. This voltage is the resistive or non-reactive componentof the feedback control voltage E of equation (9A).

It will be understood that each of multipliers 120, 121 and 122 and 135,136 and 137 gives the product of its X and Y inputs whether or not thereis propulsion, that is, whether or not, the qSA, B and C voltages arevarying sinusoidally or are frozen to instantaneous values atstandstill. A common control is thus exercised over the control signalsand suspension is maintained both at standstill and during propulsion.

It will also be understood that multipliers 120 to 122 and to 137 havesubstantially the same composition and function as the aforedescribedmultiplier 25 of FIGS. 4 and 4A and thus, like multiplier 25, are notinfluenced by the frequency of the signal inputs thereto since the pathstherethrough are essentially do. The varying frequency of the X inputsto the multipliers will thus have no effect on the magnitude of theiroutputs, and the frequency can be varied as required for vehicle speedcontrol without affecting the feedback voltage control required tomaintain suspension.

The impedance of the motor windings, however, increases with frequency,as before discussed, and it is necessary therefore to increase thefeedback voltage E accordingly so that the motor current will be of theproper strength to keep the suspension flux constant at all motorspeeds. This increase in control voltage E as a function of propulsionfrequence and speed, is provided by differentiators 143 to 145 which areconnected in parallel across their associated multipliers 135 to 137,that is, the differentiators also receive the X input signals to theirrespective multipliers and supply their outputs to the inputs of themultiplier amplifi-

1. The non-linear feedback method of linearizing the voltage vs. forcefunction of an electroresponsive force field generator whose generatedattractive force with respect to a nonmovable coacting member separatedtherefrom varies directly as the square of the generator current andinverselY as the square of the separation distance, said methodcomprising the steps of: sensing the gap defining the separationdistance and any acceleration of the generator associated with anychange in the gap to produce signals indicative of the length of the gapand the rate of change of the gap; deriving from said signals a forceproportional feedback voltage corresponding to a gap stabilizingattractive force to be generated by the generator which is sufficientagainst an opposing force thereon to restore and maintain the generatorin a position of stable equilibrium at a predetermined gap; derivingfrom said feedback voltage and said signals nonreactive and reactivefeedback voltage components respectively proportional to the length ofthe gap and the frequency of the signals; and applying to the generatora terminal voltage proportional to the sum of said non-reactive andreactive voltage components, whereby said stabilizing attractive forceis produced by the generator.
 2. The feedback method as in claim 1wherein the generator is suspended below its co-acting member and theopposing force is the weight of the generator due to the acceleration ofgravity.
 3. The feedback method as in claim 1 wherein the opposing forceis an inertial force acting on the generator.
 4. The feedback method asin claim 2 wherein the opposing force has both gravitational andinertial components.
 5. The feedback method as in claim 1 wherein theopposing force is zero in the absence of an inertial force acting on thegenerator.
 6. The feedback method as in claim 1 wherein the opposingforce is produced by an equivalent force field generator.
 7. Thefeedback method as in claim 6 wherein the equivalent generators arephysically connected together.
 8. The feedback method as in claim 7wherein the opposing forces of the equivalent generators are equal at apredetermined value in which the gaps between the generators and theirrespective co-acting members are equal.
 9. The feedback method as inclaim 7 wherein the opposing forces of the equivalent generators arezero when the gaps between the generators and their respective co-actingmembers are equal.
 10. The feedback method as in claim 4 and comprisingthe further steps of: sensing any lateral inertial force acting on thegenerator in a direction transversely to the direction of gravity actingthereon and indicative of a condition creating a need for adjustment ofsaid predetermined gap, thereby to produce signals indicative of saidlateral inertial force; and adding said last named signals to saidlength of gap and rate of gap change signals to adjust the strength ofsaid force proportional feedback voltage whereby said predetermined gapis adjusted sufficiently to satisfy said need.
 11. The feedback methodas in claim 1 wherein said step of deriving said non-reactive andreactive voltage components includes the step of electrically extractingthe square root of said force proportional voltage.
 12. The feedbackmethod as in claim 1 wherein said step of deriving said non-reactive andreactive voltage components includes the steps of electricallyextracting the square root of said force proportional voltage,electrically multiplying the square root voltage by the length of gapsignal voltage, and differentiating the square root voltage.
 13. Thefeedback method as in claim 1 wherein said step of deriving saidterminal voltage includes the step of summing said non-reactive andreactive voltage components.
 14. The feedback method as in claim 1wherein the derivation of the force proportional and terminal voltagesinvolves multiplications and summations expressed by the voltage vs.force function equation: E K3 ( Square Root F lR j Square Root F K4omega ) where: E is the terminal voltage Square Root F lR is thenon-reactive voltage component j Square Root F K4 omega is the reactivevoltage component K3, K4 are constantS j is the reaction symbol F is theattractive force; the force proportional voltage l is the gap length Ris the generator resistance omega is 2 pi f f is the sensed signalfrequency.
 15. The feedback method as in claim 1 wherein the generatoris an electromagnetic device and its generated force field is a magneticfield.
 16. The non-linear feedback method of linearizing the voltage vs.force function of a polyphase linear electric motor whose generatedmagnetic attractive force with respect to a ferromagnetic reaction railfrom which it is suspended and physically separated varies directly asthe square of the motor current and inversely as the square of theseparation distance, said method comprising the steps of: sensing thegap defining the separation distance and any acceleration of the motorassociated with any change in the gap to produce signals indicative ofthe length of the gap and the rate of change of the gap; deriving fromsaid signals a force proportional feedback voltage corresponding to agap stabilizing attractive force to be produced by the motor which issufficient against an opposing force acting on the motor to restore andmaintain the same in a position of stable equilibrium at a predeterminedgap; operating a constant amplitude variable frequency polyphase controlvoltage; deriving from said force proportional voltage, from saidsignals and from said polyphase voltage per phase thereof non-reactiveand reactive feedback voltage components respectively proportional tothe length of the gap and the frequency of the polyphase voltage; andapplying to the motor a polyphase terminal voltage which is proportionalfor each phase thereof to the sum of said non-reactive and reactivevoltage components, thereby to produce said stabilizing attractive forceat any frequency upwards from zero of said polyphase control voltage.17. The feedback method as in claim 16 wherein the magnetic field of themotor suspends and propels the same along the rail and wherein the motorlinear speed along the rail is a function of the frequency of themagnetic field alternations.
 18. The feedback method as in claim 17wherein the reactive voltage component for each phase is proportional tothe first derivative of the product of said constant amplitude variablefrequency, polyphase control voltage and the square root of said forceproportional voltage, and the nonreactive voltage component for eachphase is proportional to the product of the gap length times the squareroot of the force proportional voltage times said polyphase controlvoltage.
 19. The feedback method as in claim 18 wherein the products andsummations are expressed by the voltage vs. force function equation: EK1 ( Square Root FMlR + j Square Root FM K2f) where: E is the polyphasealternating current terminal voltage Square Root FM lR is thenonreactive voltage component j Square Root FM K2f is the reactivevoltage component FM is the attractive force between the motor and therail; the force proportion voltage l is the gap length R is the motorwinding resistance f is the frequency of the terminal voltage K1, K2 areconstants.
 20. The method of combined suspension and propulsion of anelectric linear motor support for a high speed tracked transport vehiclewhich comprises the steps of disposing an electric linear motor below amagnetic rail support therefor, controlling the voltage and currentrelationship of the motor to establish an attractive magnetic fieldbetween the motor and rail sufficient to suspend the mass including themotor and its load against the force of gravity and at a selected gapdefining the displacement of the motor from the rail, sensing the gapdisplacement and any acceleration of said mass assOciated with anychange in the gap displacement, adjusting said voltage and currentrelationship of the motor in response to signals sensed by thedisplacement and acceleration sensors to maintain said selected gapdisplacement, adjusting said voltage and current relationship to producealternations of the suspension field and to move the same along themotor and in linear thrust producing relation to the rail to move themass along the rail at a speed determined by the frequency of said fieldalternations, varying the frequency of said field alternations to adjustthe linear speed of the mass, and adjusting said voltage and currentrelationship as a function of frequency to compensate for increasingmotor impedance with frequency thereby to maintain the strength of thesuspension field constant at all propulsion speeds.
 21. A feedbackcontrol system comprising: a fixed member; an electroresponsive forcefield generator separated in free space at a predetermined separationdistance from said fixed member for generating a force field therewithand resultant attractive force therebetween wherein the attractive forcevaries as the square of the generator current and inversely as thesquare of the separation distance; means carried by the generator forproducing a force proportional voltage proportional to the attractiveforce which is required to be generated by the generator to restore andmaintain the same in stable equilibrium at said predetermined separationdistance against an opposing force acting on the generator; and meansresponsive to said force proportional voltage for producing and applyingto said generator a terminal voltage sufficient to enable the same togenerate said required attractive force.
 22. A feedback system as inclaim 21 wherein said terminal voltage producing means includes: squarerooter means for electrically producing a square root voltage which isthe square root of said force proportional voltage.
 23. A feedbackcontrol system as in claim 21 wherein: said force proportional voltagemeans includes sensing means for producing a signal proportional to theseparation distance; and said terminal voltage producing means includes:square rooter means for electrically producing a square root voltagewhich is the square root of said force proportional voltage; andmultiplier means for electrically producing a voltage which is theproduct of said square root voltage and said distance proportionalsignal.
 24. A feedback control system as in claim 23 wherein: saidsquare root voltage has a frequency proportional to any variations insaid distance proportional signal; and said terminal voltage producingmeans also includes: means for differentiating said square root voltageto produce a voltage proportional to its frequency; and means forelectrically summing said product voltage and said frequencyproportional voltage.
 25. A feedback control system as in claim 24wherein said terminal voltage is produced in accordance with theequation: E K1 F (Rl jK2f) where: E is the terminal voltage F is therequired attractive force R is the generator resistance l is theseparation distance f is the frequency of the square root voltage K1 andK2 are constants.
 26. A suspension apparatus having a force generator, aco-acting support therefor, a feedback circuit for controlling asuspension force produced by said force generator to suspend the same infree space from said support therefor without contact therewith andagainst the force of gravity acting thereon to thereby maintain thegenerator in a state of stable equilibrium at a selected gap lengthwithin a range of selectable gap lengths between said generator andsupport, said feedback circuit having at least one input selected from agroup of inputs which respectively represent the position, velocity andacceleration of the generator associated with any change in the gap, anoutput signal applicable to said force generator to control saidsuspension force, and circuit means responsive to said inputs to producesaid output signal.
 27. An apparatus according to claim 26, wherein saidfeedback circuit includes means for setting the magnitude of thesuspension force sufficient to counterbalance the force of gravity at apreselected nominal gap within said range of gaps.
 28. An apparatusaccording to claim 26 wherein the magnitude of the suspension force isregulated by sensing the vertical position of the generator and theacceleration of change of that position.
 29. An apparatus according toclaim 26, wherein said circuit means includes an element having anoutput proportional to a mathematical root of the input thereto.
 30. Anapparatus according to claim 26, wherein said circuit means includes anelement having an output proportional to a mathematical differential ofthe input thereto.
 31. A feedback circuit for controlling the voltage ofan electroresponsive force field generator which is attracted by itsforce field toward a co-acting member and held physically separatedtherefrom by an opposing force thereon wherein the generator ismaintained at a preselected separation distance when the attractive andopposing forces are equal and wherein the attractive force variesinversely as the square of the separation distance and directly as thesquare of the generator current, said feedback circuit comprising afirst input having X signals which vary with the displacement distanceand a second input having signals which vary with any acceleration ofthe generator associated with any change in the separation distance, andoutput having a feedback voltage for controlling the generator voltageto maintain the attractive force equal to the opposing force, and meansresponsive to the signals of said first and second inputs for producingsaid feedback voltage.
 32. A suspension-propulsion feedback systemcomprising: a ferromagnetic support rail having linear thrust producingreaction means; an electric linear motor disposed beneath said rail inspaced relation therewith defining an air gap therebetween, said motorhaving plural phase windings for producing a combined motor suspensionand propulsion magnetic field with respect to said rail and its reactionmeans; a controllable plural phase power amplifier source of variableamplitude and variable frequency voltage for respectively energizingsaid plural phase windings; and gap length and frequency control meanscarried by said motor for simultaneously regulating the amplitude ofeach phase of said energizing voltage to restore and maintain the motorin stable equilibrium at a predetermined gap and for simultaneouslyregulating the frequency of each phase of said energizing voltage to setthe linear speed of the motor along the rail.
 33. A feedback system asin claim 32 wherein said gap length control means includes: means forsensing the gap length and any acceleration of the motor associated withany change in the gap length.
 34. A feedback system as in claim 33wherein said gap length control means also includes: means responsive tosignals produced by said sensing means for producing a feedback voltageinput to said power amplifier source to regulate the amplitude of itsoutput voltage.
 35. A feedback system as in claim 34 wherein said signalresponsive means includes: operational amplifier means responsive tosaid signals for producing a force proportional voltage which isproportional to the magnetic motor-to-rail attractive force required tomaintain the motor at said predetermined gap against the force ofgravity acting thereon; and means for electrically extracting the squareroot of said force proportional voltage to produce a square rootvoltage.
 36. A feedback system as in claim 35 wherein: said frequencycontrol means comprisEs a plural phase source of constant amplitude andvariable frequency control; first multiplier means for electricallyproducing per phase of said control voltage an output which is theproduct of the control voltage amplitude times said square root voltage;second multiplier means for electrically producing per phase of saidcontrol voltage the product of said first multiplier means output timesthe length of gap signal to produce a gap compensated control voltagecomponent; means for differentiating per phase of said control voltagethe product output of said first multiplier means to produce a frequencycompensated control voltage component; and means per phase of saidcontrol voltage for electrically summing said gap and frequencycompensated voltage components.
 37. A feedback system as in claim 36including means for simultaneously varying the frequency per phase ofsaid control voltage.